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Mean-Squared Error Estimation in Transformed Fay–Herriot Models

https://doi.org/10.1111/j.1467-9868.2006.00542.x

Slud, Eric V. ; Maiti, Tapabrata ( March 2006 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

Summary
The problem of accurately estimating the mean-squared error of small area estimators within a Fay–Herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable. For bias-corrected empirical best linear unbiased predictor small area point estimators, mean-squared error formulae and estimators are provided, with biases of smaller order than the reciprocal of the number of small areas. The performance of these mean-squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the US Census Bureau's on-going ‘Small area income and poverty estimation’ project.

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